Are some people more prone to getting finger pain?

Finger pain: Common causes of finger pain include injury or trauma, such as bending your finger backward (hyperextension) or from repetitive use, such as long periods of keyboarding. More serious conditions, such as diabetes or a neck or spinal cord injury, can also cause pain or a burning sensation in your fingers. Sore joints in the fingers may be caused by arthritis, inflammation, and age-related wear.

Yes : If you mean arthritis which has a genetic factor.